You should seek a dental evaluation as soon as possible. The most likely cause of the red bump may be trauma from the broken tooth. There may be a sharp spot on the tooth that's rubbing your tongue a little raw and making it red. You should really take care of that broken tooth before it gets worse and can result in an abscess where the infection spreads.
As for the pain, its possible you may have something going on with the other tooth as well or what we term, referred pain. Referred pain is when there's pain in one area but it feels like its somewhere else due to the complexities of the nervous system of the head.